Maximum Likelihood Estimate and Logistic Regression simplified

Least squares regression can cause impossible estimates such as probabilities that are less than zero and greater than 1.So, when the predicted value is measured as a probability, use Logistic Regression We use the log of the odds rather than the odds directly because an odds ratio cannot be a negative number--but its log can be negative. Notice that we have randomly initialized our coefficients for income and other predictors. These will be adjusted by Solver based on a likelihood function.We will cover them later Column H tells us the predicted probability of the borrower's actual behavior, whether that behavior is repayment or default--not simply, as in Column G, the predicted probability of defaulting on the loan. One property of logarithms is that their sum equals the logarithm of the product of the numbers on which they're based The logarithms of probabilities are always negative numbers, but the closer a probability is to 1.0, the closer its logarithm is to 0.0. I haven't covered cross-validation, which is commonly used to validate a logistic regression equation.If you don't always have a large number of cases to work with, a different approach is to use statistical inference.